Ex.13.1 Q1 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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Question

 Following are the car parking charges near a railway station up to

\(4\) hours           ₹\(60\)

\(8\) hours           ₹\(100\)

\(12\) hours        ₹\(140\)

\(24\) hours        ₹\(180\)

Check if the parking charges are in direct proportion to the parking time.

  

Text Solution

   

What is Known?

Parking charges for different hours.

What is Unknown?

Parking charges are direct proportion to the parking time or not.

Reasoning:

If two quantities are related in such a way that an increase in one lead to a corresponding proportional increase in the other, then such a variation is called direct variation.

Steps:

The parking charge for \(1\) hour in all the four cases then the variation is direct.

We have:

\[\begin{align}\frac{{60}}{4}&=\frac{{15}}{1}\\&=15\\\frac{{100}}{8}&=\frac{{25}}{2}\\ &= 12.5\\\frac{{140}}{{12}} &=\frac{{35}}{3}\\&=11.67\\\frac{{180}}{{24}}&=\frac{{15}}{2}\\&= 7.50\end{align}\]

Since all the values are not the same, the parking charges are not in direct proportion to parking times.